I suppose the athlete would need to wear an EVA suit (or a diving suit? the requirements are sort of between the two), so that'd be a bit of a damper on their peak performance, but still.
Of course, that sounds more like a skill involving reduction of friction and outputting as much power through the legs as possible than the more difficult act of also controlling a bike at those speeds.
With rollers (what I'd think the "treadmill" discussed above actually is), and a normal road bicycle, you can feel, or at least hear, the resistance just from the spokes in a spoked wheel when you really get get them spinning "real world" fast.
On fancier road race wheels, the spokes are "bladed" for this reason - their cross section is flattened to minimise aerodynamic drag. Remember that when you're riding a bike in normal conditions, the top of the wheel is hitting the oncoming air at up to twice the speed of the bike. Though, there's also a substantial amount of appearance/marketing/armchair-engineering around...
Even amateur cyclists often use "aero wheels" that no longer have spokes. They make a difference in the wind or at 20mph.
I don't think this is feasible with today's wind tunnels, though.